Research Profile

My research activity focuses on variational problems with applications to materials science, in particular in elasticity and plasticity. One key theme is the elastic behavior of thin sheets. The starting point was a variational analysis of blistering in thin films [1], which contributed to a new understanding of the origin of microstructure in these systems. I then turned to the situation where compressive Dirichlet boundary conditions by confinement, as in an obstacle problem. The optimal scaling turned out to be different, being proportional to the thickness to the power [3]. A second line of thought focused on variational models in crystal plasticity and their relaxation. An explicit relaxation of a geometrically linear model in which finitely many slip systems are active was obtained in [4], and applied to simulate numerically an indentation test in [5]. At a finer scale, a line-tension model for dislocations was derived in [10,7].

Future work will address interaction between different defects, such as damage and fracture, or density of interstitials and motion of dislocations. At the same time I intend to address microstructure formation in situations which cannot be addressed purely by energy minimization, such as plastic deformation under non-monotonous loadings, or fracture propagation, or cycling in phase transformation in shape-memory alloys. This will involve both the study of path-dependence in inelastic deformation and the study of hysteresis, and can be attacked by macroscopic rate-independent models or at a more microscopic level using transition-state theory.

Contribution to Research Areas

Research Area BMy research activity focuses on variational problems with applications to materials science, in particular in elasticity and plasticity. One key theme is the elastic behavior of thin sheets. The starting point was a variational analysis of blistering in thin films [1], which contributed to a new understanding of the origin of microstructure in these systems. A simplification of the blistering model leads to the scalar Aviles-Giga functional, which was studied in [2]. I then turned to the situation where compressive Dirichlet boundary conditions by confinement, as in an obstacle problem. The optimal scaling turned out to be different, being proportional to the thickness to the power [3].

A second line of thought focused on variational models in crystal plasticity and their relaxation. An explicit relaxation of a geometrically linear model in which finitely many slip systems are active was obtained in [4], and applied to simulate numerically an indentation test in [5]. The situation in a geometrically nonlinear setting is considerably more subtle. The relaxation for an elastically rigid problem with one-slip-system was obtained in [6]. At a finer scale, self-similar dislocation microstructures have been related to Hall-Petch effect [4] and a line-tension model for dislocations was derived in [7]. The study of models of brittle fracture required a detailed analysis of the space SBD [8].
In the geometrically nonlinear setting, the microscopic significance of the multiplicative decomposition in crystal plasticity was discussed in [9].